A spectral/ <i>hp</i> element method for thermal convection

We report on a high-fidelity, spectral/hp element algorithm developed for the direct numerical simulation of thermal convection problems. consider incompressible Navier–Stokes (NS) and advection–diffusion equations coupled through body-forcing term. The flow is driven by prescribed flowrate forcing with explicit treatment nonlinear advection terms. body-force term also decouples both NS equations. problem then temporally discretized using an implicit–explicit scheme in conjunction velocity-correction splitting to decouple velocity pressure fields momentum equation. Although not unique, this type discretization has been widely applied problems we therefore provide comprehensive overview implementation which available open-source package Nektar++. After verifying number illustrative apply code investigate channel uniform or streamwise sinusoidal lower wall, addition patterned heating. verify solver against previously published two-dimensional results. Finally, first time three-dimensional wall heating which, chosen parameter, leads unusual dynamics initially unsteady instability leading steady saturated state.